Algebra & Algebraic Geometry Seminar-Jeremy Usatine-Motivic integration for Artin stacks

Date/Time
Date(s) - 12/01/2023
10:30 am - 11:30 am

Abstract: A standard method for studying a singular variety is to resolve
it by a smooth variety and to then relate invariants of the singular variety
to invariants of the smooth one. Motivic integration provides powerful tools
for obtaining such a relationship. Motivated by the McKay correspondence, I
will describe a context in which interesting varieties admit natural resolutions
of singularities by Artin stacks. This suggests a need for versatile tools in
studying these “stacky” resolutions of singularities. I will discuss joint work
with M. Satriano in which we use motivic integration to provide such tools,
and I will also explain how our work leads to a notion of crepantness for stacky
resolutions of singularities.

Location:  Hamilton Hall, Room 207